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THESIS

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METAMATERIAL FOR RADAR FREQUENCIES

by

Szu Hau Tan

September 2012

Thesis Advisor: David C. Jenn Second Reader: James Calusdian

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4. TITLE AND SUBTITLE Metamaterial for Radar Frequencies 5. FUNDING NUMBERS 6. AUTHOR(S) Szu Hau Tan

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13. ABSTRACT (maximum 200 words)

The objective of this thesis is to investigate a new design of periodic metamaterial (MTM) structure for radar cross-section (RCS) reduction application on aircraft and ships. MTMs are man-made materials, not found in nature, that exhibit unusual properties in the radio-, electromagnetic-, and optical-wave bands. The cells of these periodic MTM structures must be much smaller than the wavelength of the frequency of interest. In a MTM, the structure and dimensions of the design at the frequency of interest can produce negative values of permeability and/or permittivity, which define the electrical properties of the MTM. This study looks at various designs of absorbing layers presented in technical papers and verifies the results in simulations. Modifications are done to the existing designs to achieve good absorption level at the radar-frequency band of interest. Modeling and simulation are done in Microwave Studio by Computer Simulation Technology (CST). The S-parameters S11 (reflection coefficient) and S12 (transmission coefficient) are used to investigate the performance of the MTM as a radar-frequency absorber. 14. SUBJECT TERMS Metamaterials, Negative Index, Radar Cross Section, Permittivity and Permeability.

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Approved for public release; distribution is unlimited

METAMATERIAL FOR RADAR FREQUENCIES

Szu Hau Tan Civilian, Singapore Technologies Aerospace Ltd.

B.S., University of Glasgow, 1998.

Submitted in partial fulfillment of the requirements for the degree of

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

from the

NAVAL POSTGRADUATE SCHOOL September 2012

Author: Szu Hau Tan

Approved by: David C. Jenn Thesis Advisor

James Calusdian Second Reader

R. Clark Robertson Chair, Department of Electrical and Computer Engineering

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v

ABSTRACT

The objective of this thesis is to investigate a new design of periodic metamaterial

(MTM) structure for radar cross-section (RCS) reduction application on aircraft and

ships. MTMs are man-made materials, not found in nature, that exhibit unusual properties

in the radio-, electromagnetic-, and optical-wave bands. The cells of these periodic MTM

structures must be much smaller than the wavelength of the frequency of interest. In a

MTM, the structure and dimensions of the design at the frequency of interest can produce

negative values of permeability and/or permittivity, which define the electrical properties

of the MTM. This study looks at various designs of absorbing layers presented in

technical papers and verifies the results in simulations. Modifications are done to the

existing designs to achieve good absorption level at the radar-frequency band of interest.

Modeling and simulation are done in Microwave Studio by Computer Simulation

Technology (CST). The S-parameters S11 (reflection coefficient) and S12 (transmission

coefficient) are used to investigate the performance of the MTM as a radar-frequency

absorber.

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TABLE OF CONTENTS

I. INTRODUCTION........................................................................................................1 A. BACKGROUND ..............................................................................................1 B. LITERATURE REVIEW ...............................................................................5

1. Historical Background.........................................................................5 C. THESIS OBJECTIVE .....................................................................................7 D. THESIS OUTLINE ..........................................................................................7

II. METAMATERIALS ...................................................................................................9 A. INTRODUCTION............................................................................................9 B. DOUBLE-NEGATIVE MATERIAL .............................................................9 C. RETRIEVAL OF AND FROM S11 AND S21 .....................................11 D. NEGATIVE REFRACTION AND LEFTHANDEDNESS ........................12 E. SPLIT-RING RESONATOR ........................................................................13 F. SUMMARY ....................................................................................................15

III. MODELING AND SIMULATION SETUP ............................................................17 A. INTRODUCTION..........................................................................................17 B. CST MICROWAVE STUDIO (MWS) ........................................................17 C. BASELINE DESIGN .....................................................................................18 D. OTHER BOUNDARY CONDITIONS ........................................................21

1. Periodic Boundary Condition ...........................................................22 2. Unit-cell Boundary Condition ...........................................................22

E. PORTS ............................................................................................................22 F. THE REFERENCE PLANE .........................................................................24

IV. SIMULATION RESULTS AND DATA ANALYSIS .............................................27 A. DESIGN (C) ....................................................................................................27

1. Length of Wire ...................................................................................28 2. Width of Wire .....................................................................................30 3. Thickness of Wire and Separation Distance Between Unit Cells ..32 4. Number of Layers ..............................................................................34 5. Conductor Width ...............................................................................36 6. Conductor Thickness .........................................................................38 7. Center Conductor ..............................................................................39 8. Gap ......................................................................................................40 9. Overall Performance .........................................................................41

B. DESIGN (E) ....................................................................................................46 C. SUMMARY ....................................................................................................47

V. RECOMMENDATIONS AND CONCLUSION .....................................................49 A. SUMMARY AND CONCLUSIONS ............................................................49 B. RECOMMENDATION FOR FUTURE STUDIES ....................................50

1. EM Transparent Material Between Unit Cells ...............................50 2. Dual-Polarization Design...................................................................51

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3. Wideband Absorption .......................................................................51 4. Circuit Equivalent of Design (c) .......................................................51 5. Extracting and from Scattering Parameters S11 and S12 .......52

LIST OF REFERENCES ......................................................................................................53

INITIAL DISTRIBUTION LIST .........................................................................................57

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LIST OF FIGURES

Figure 1. (a) Example of a material’s measured negative permittivity and (b) negative permeability. Notice that both permittivity and permeability are negative at the resonant frequency (From [6]). ..................................................4

Figure 2. Metamaterial made up of a structure of split-ring resonators and wires. Cell size of each SRR is much smaller than (From [11]). ..............................5

Figure 3. (a) Planar LH distributed periodic structure and its (b) unit cell (From [12])....................................................................................................................6

Figure 4. Obliquely incident wave propagation from DPS-DNG-DPS. Notice that the wave bends to the same side as the incident wave (After [19]). ................12

Figure 5. Cylinders with internal structures. Metallic films separated by distance d. There is a small gap at every film that prevents current from flowing around the “ring” (From [20])..........................................................................14

Figure 6. Plan view of the cylinder. When the cylinder encounters a magnetic field parallel to it, current is induced. Current is proportional to the capacitance of the structure (After [20]). .............................................................................14

Figure 7. (a) A front view of the resonator, (b) back view of the wire and (c) oblique view of the unit cell with direction of propagation in z (From [22]). ..............18

Figure 8. (a) Setup of the boundary conditions and (b) background properties used in MWS simulations (From [21]). ...................................................................20

Figure 9. Several variations of the baseline design (a)–(f) that were tested. As shown here, three pieces of each design were simulated with waveguide ports. ........21

Figure 10. Two-port configuration used to compute the S11 and S12 parameters. .............23 Figure 11. Single port configuration used to compute S11 for a coating application. .......23 Figure 12. (a) Definition of waveguide port 1. (b) Definition of waveguide port 2. ........24 Figure 13. Design (c): the final design. .............................................................................28 Figure 14. Simulated S-parameters for a wire of 7.8 mm in length. .................................29 Figure 15. Simulated S-parameters for a wire of 11.8 mm in length (optimum). .............29 Figure 16. Simulated S-parameters for a wire of 15.8 mm in length. ...............................30 Figure 17. Simulated S-parameters for a wire width of 1.7 mm, as used in [22]. .............31 Figure 18. Simulated S-parameters for a wire width of 1.0 mm. ......................................31 Figure 19. Simulated S-parameters for a wire width of 0.64 mm. ....................................32 Figure 20. Simulated S-parameters for a wire width of 0.5 mm. ......................................32 Figure 21. Simulated S-parameters for a wire thickness of 0.017 mm with unit-cell

separation of 0.65 mm......................................................................................33 Figure 22. Simulated S-parameters for a wire thickness of 0.15 mm with unit-cell

separation of 1.7 mm........................................................................................33 Figure 23. Simulated S-parameters for a wire thickness of 0.35 mm with unit-cell

separation of 2.0 mm........................................................................................34 Figure 24. Simulated S-parameters for two layers. ...........................................................35 Figure 25. Simulated S-parameters for three layers. .........................................................35 Figure 26. Simulated S-parameters for four layers. ..........................................................36 Figure 27. Simulated S-parameters for a conductor width of 0.6 mm. .............................36

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Figure 28. Simulated S-parameters for a conductor width of 0.8 mm. .............................37 Figure 29. Simulated S-parameters for a conductor width of 1.0 mm. .............................37 Figure 30. Simulated S-parameters for a conductor thickness per original design,

0.017 mm. ........................................................................................................38 Figure 31. Simulated S-parameters when the conductor thickness is increased to 0.05

mm. ..................................................................................................................38 Figure 32. Simulated S-parameters per design in [22]. ....................................................39 Figure 33. Simulated S-parameters per design in [22], but with center conductor

extension of 1 mm. ...........................................................................................39 Figure 34. Simulated S-parameters per design in [22], but with center conductor

extending 2 mm................................................................................................40 Figure 35. Simulated S-parameters for a gap of 0.3 mm in the design. ............................40 Figure 36. Simulated S-parameters for a gap of 0.606 mm in the design. ........................41 Figure 37. Simulated S-parameters for a gap of 1.0 mm in the design. ............................41 Figure 38. Coordinate system definition for non-normal incidence angles. .....................42 Figure 39. Magnitude of S11 at different θ with = 0o. ....................................................44 Figure 40. Magnitude of S11 at different with θ = 0o. ....................................................44 Figure 41. Magnitude of S11 when θ equals . ..................................................................44 Figure 42. (a) Design (c) with metallic backing, a configuration likely during

application on a platform. (b) Result from this configuration. S11 has a value equivalent to a reduction of 33.75 dB. S12 is zero, due to the metallic backing, no transmission through a metallic surface. ......................................45

Figure 43. Simulated S-parameters for S11 and S21 of Design (e). ....................................47 Figure 44. (a) Side view of material. (b) Plan view of material. Design (c)

incorporated with EM transparent material spacer. (a) and (b) simulate a large sheet of the metamaterial with Design (c) cascaded horizontally and vertically. .........................................................................................................50

Figure 45. Possible designs for dual polarization. .............................................................51 Figure 46. A possible circuit-equivalent model to Design (c). .........................................52

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LIST OF TABLES

Table 1. Radar-frequency bands and some military applications (From [1]). .................1 Table 2. Value of parameters used in the design from [22]. ..........................................19 Table 3. Final parameters used in simulation for the results of Design (c).

Parameters are defined in Figure 7. .................................................................27 Table 4. Magnitude of reflected EM wave for oblique incidence on Design (c). ..........43 Table 5. Parameters used in the simulation of Design (e). ............................................46

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LIST OF ACRONYMS AND ABBREVIATIONS

ADS Advance Design System

CPR Coplanar Ring

CST Computer Simulation Technology

DNG Double Negative Material

DPS Double Positive Material

EM Electromagnetic

ERR Electric Ring Resonator

FIT Finite Integration Technique

LH Left-Handed

MTM Metamaterial

MWS Microwave Studio by CST

NIM Negative Index Material

OTH Over-The-Horizon

PCB Printed Circuit Board

RAM Radar Absorbing Material

RCS Radar Cross Section

SNR Signal-to-Noise Ratio

SNG Single-Negative

SRR Split Ring Resonator

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EXECUTIVE SUMMARY

Since the invention of radar, attempts to counter radar detection have been investigated.

There are four basic ways to do this: (a) shaping of the platform, (b) application of radar-

absorbing material to the platform, (c) disrupting the radar’s receiver by electronic

jamming and (d) flying under the radar. Option (a) can only be realized at the platform’s

design stage. Existing platforms without shaping incorporated into the design can only

use options (b), (c) and (d). The problem with option (b) is the weight involved. Radar-

absorbing material (RAM) usually consists of iron powder as inclusions in a primary

binding matrix like polyurethane. Additional weight on an aircraft is a big issue because

it compromises the amount and type of armaments that can be carried. Option (c) also

reduces the amount of weaponry an aircraft can carry. Option (d) is not always feasible,

as it may be geographically impossible and only avoids ground radars at best.

In this thesis, the objective of the study was to design a new metamaterial (MTM)

for application to platform surfaces. The MTM will be a radar absorber to reduce the

platform’s radar cross-section (RCS) signature, thereby making the platform less

detectable at long range by C- and X-band radars. The MTM will be lighter than

conventional RAM coatings since it contains no iron inclusions and can be made much

thinner.

Materials are electrically defined by their permittivity and permeability. Most

naturally occurring material possesses positive permittivity and permeability, but a

MTM’s permittivity and permeability can have either one or both negative. MTMs are

man-made materials that possess interesting properties like negative index of refraction

that bend electromagnetic (EM) waves to the same side of the normal as the incident

wave when the EM wave travels through them, reversing Snell’s law of refraction.

Much research on MTM is based on the split-ring resonator, developed by Pendry

et al. in 1999 [1]. The objective of this study was to find a new MTM design, departing

from the traditional approach. This research is based on a design presented in [2], which

describes a MTM with almost complete absorption. The design was replicated in

Microwave Studio (MWS) by Computer Simulation Technology (CST). The results

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obtained in the simulations were in good agreement with the reported results with regard

to the frequency dependence of the absorption and its level.

Modifications to the design in [2] were made to adjust the frequency and improve

the absorption. The original design is a free standing surface; that is, it operates with free

space on both sides. The configuration was modified so that it could be placed on a

conducting surface. Six new designs, made up of basic coplanar rings and cut wires, were

tested, but only two gave promising results. One of the promising modifications, Design

(c), depicted in Figure 1, was tested extensively, and the parameters in the unit cell were

optimized for better performance. The parameters of the unit cell of Design (c) are shown

in Table 1. Detailed simulation settings are provided in Chapter III. The u, v and w axes

in Figure 1 refer to the working coordinate system and correspond to the x, y and z axes,

respectively, in the global coordinate system.

(a) (b) (c) Figure 1. Unit-cell design for Design (c)

During the course of optimization of Design (c) in simulations, it was found that

certain parameters are able to shift the frequency of absorption around the selected

frequency band. The first of these parameters is the width of the cell W, because it is

1a

2a H

W

t

G

Wire L

Center Conductor Length

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proportional to the wavelength and determines in which frequency band the absorption

lies. Other parameters, like width of wire, thickness of wire, separation distance between

unit cells, conductor width, and length of center conductor can also affect the absorption

frequency, but these parameters are used to fine tune the frequency and the absorption

level within the frequency band.

Table 1. Parameters used in Design (c) simulations.

Parameter Dimension (mm)

1a 4.2

2a 12.0

W 3.9

G 0.606

t 0.8

L 0.64

H 11.8

Center Conductor Length 6.0

Conductor thickness 0.017

Substrate thickness 0.2

Wire thickness 0.15

Separation distance between unit cell 1.7

Number of unit cell layers 3 pieces

The two-port simulation result of Design (c) is shown in Figure 2. The result was

comparable to the result reported in [2]. A reflection coefficient (scattering parameter

S22) of 0.0418 (27.57 dB) and transmission coefficient (scattering parameter S12) of

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0.0637 (23.91 dB) were achieved. The simulated result of Design (c) on a

conducting surface was shown in Figure 3. It achieved a reflection coefficient of 0.02053

(33.75 dB).

Figure 2. The two port simulation result of Design (c). Reflection coefficient of 0.0418 (27.57 dB) and transmission coefficient of 0.0637 (23.91 dB).

Figure 3. The result of Design (c) on a conducting surface. Reflection coefficient of

0.0205 (33.75 dB).

The objective of this study was to find a new MTM design for X-band radar

frequencies that could be applied to a metallic surface. Hence, the design, modeling and

simulation of a new MTM, which was a modification of the design in [2] is described in

this thesis. A detailed description of Design (c) was given, with dimensions as in Table 1.

S-Parameter [Magnitude]


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During the course of this study, new questions were raised that need to be

addressed in future research. It has been shown with Design (e) that better performance in

some areas is possible. The recommended areas for future investigation are:

1. Simulation with a low density spacer between the dielectric layers.

2. Design a dual-polarization MTM.

3. Improve the bandwidth.

4. Derive an equivalent circuit for Design (c).

5. Extract the effective and of the structure from simulated scattering

parameters S11 and S12.

6. Extend the design to be effective for other than normal incidence.

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EXECUTIVE SUMMARY REFERENCES

[1] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from Conductors and Enhanced Nonlinear Phenomena”, IEEE Trans. Microwave Theory Tech., vol 47, no.11, pp. 2075-2084, November 1999.

[2] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect

Metamaterial Absorber”, Phys. Rev. Letters, vol. 100, paper 207402, 2008.

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ACKNOWLEDGEMENTS

I would like to take this opportunity to thank my company, Singapore

Technologies Aerospace Limited, for giving me this wonderful opportunity to further my

studies at the Naval Postgraduate School, Monterey, California.

I would also wish to express my utmost gratitude to Professor David C. Jenn of

the Naval Postgraduate School for being my thesis advisor and for his patience and

guidance in seeing me through the completion of this thesis. I thank Dr. James Calusdian

for being my second reader for this thesis and accommodating to my schedule.

Most of all, I cannot sufficiently thank my supportive wife, who came with me to

Monterey, for all the things that she has done to allow me to concentrate on my studies

and for her good job in taking care of our two wonderful children.

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1

I. INTRODUCTION

A. BACKGROUND

The principle of radar works by transmitting an electromagnetic (EM) wave and

detecting a reflected echo from the target. If there is a target present with sufficient

signal-to-noise ratio (SNR), then a detection is declared. Every target has a signature. In

the radar world, this signature is known as the radar cross section (RCS). The RCS is the

collective scattering from all the contributors on the platform. Military radars are

classified into search and surveillance or targeting radars. For over-the-horizon (OTH)

surveillance, low frequencies like HF to UHF bands are used (Table 1). These

frequencies have long wavelengths which can propagate very long distances. Mid-range

surveillance radars use higher frequencies like L or S-band. The C and X-band radars are

used for tracking because they offer better down-range and cross-range resolution.

Table 1. Radar-frequency bands and some military applications (From [1]).

2

The C- and X-bands are the frequency bands of interest in this research because

they are used for tracking and short range search radar. If long-range surveillance radar

can detect a target, but the tracking radar cannot track and pinpoint the target, the attacker

will not be able to fire the weapon.

One way of reducing the signature of an existing platform is by the use of radar

absorbing material (RAM). A major issue with RAM coatings is the weight. These

materials consist of iron powder as inclusions in a primary binding matrix like

polyurethane. However, to achieve the required absorption, the thickness and weight of

conventional material is too large. One possible solution for overcoming the weight and

volume issues is to use new engineered metamaterials (MTMs). MTMs are man-made,

macroscopic, composite materials that possess properties not found in nature. They are

comprised of “cells” with inclusions that take on many forms, such as spheres and rings.

If the cells are small compared to wavelength, then the material is effectively

homogeneous. These materials are designed and structured to manipulate the propagation

of electromagnetic waves that impinge on them. An application for MTMs that many

researchers are looking into is platform cloaking, rendering a platform invisible and

undetectable by radar [2–4].

If a platform is covered with MTMs designed to work in the radar’s frequency

range, the EM wave from the radar will either be directed around the platform and

continue its path (cloaking) or be completely absorbed by the MTM. In the second

scenario, the MTM works as a radar-absorbing material. Either way, the RCS of the

platform is reduced, as no EM wave is reflected back to the radar. Thus, monostatic radar

will not detect the presence of a platform.

Electrically, materials are defined by their permittivity ε and permeability ,

which are complex quantities in the frequency domain:

( )o r o r rj (1.1)

( )o r o r rj (1.2)

3

where 0 = 8.85410-12 F/m is the permittivity of free space and 0 = 410-7 H/m is the

permeability of free space. Here the j te time convention is used. The complex index of

refraction of the material is:

r rn . (1.3)

MTMs can have a negative refractive index. For a lossless material

( 0r r ),

r rn . (1.4)

If both r and r are negative, they are called negative-index materials (NIM), also

known as double-negative material (DNG). DNG materials have some unique

propagation characteristics, as will be discussed in the next chapter.

Permittivity and permeability are the two parameters that determine an MTM’s

response to EM waves. Most natural materials have positive relative permittivity and

permeability. Some materials have negative permittivity or permeability [5]. At the

resonant frequency of a DNG MTM, both permittivity and permeability are negative, as

shown in Figure 1, resulting in a negative refractive index. Among the unique EM

propagation properties of DNG materials is that the phase fronts propagate in a direction

opposite to the power flow given by the Poynting vector. This has led to the designation

of DNG material as left-handed (LH) materials.

Permittivity and permeability can be determined by measuring the complex

(magnitude and phase) EM wave reflection and transmission coefficients of a material

sample. For several reasons, difficulties arise in obtaining permittivity and permeability

when the material under test is a MTM. One is that the properties of a MTM are

frequency dependent. In measuring the coefficients, a sweep of frequencies is used so

that the resonant frequency can be found. Waveguide measurement is preferred, because

large samples, which take time and money to fabricate, are not required. In free space

there is diffraction around the edges of the test sample and wave interactions with other

objects and the environment, which lead to measurement errors.

4

(a)

(b)

Figure 1. (a) Example of a material’s measured negative permittivity and (b) negative permeability. Notice that both permittivity and permeability are negative at the

resonant frequency (From [6]).

5

When the MTM’s inclusion dimensions (cell sizes) are much smaller than the

wavelength of the EM wave, the MTM can be homogenized as a medium with effective

dielectric and magnetic properties [7]. Although “small” generally refers to much less

than the wavelength , cell sizes of up to 0.25 have been used. A “two-dimensionally”

isotropic MTM made of coplanar rings and wires is shown in Figure 2.

Figure 2. Metamaterial made up of a structure of split-ring resonators and wires. Cell size of each SRR is much smaller than (From [11]).

B. LITERATURE REVIEW

1. Historical Background

In 1967, V. G. Veselago investigated theoretically the interaction of a plane wave

on a material with negative permittivity and permeability [8]. He believed that such a

homogeneous material could be fabricated with a semiconductor. There was no

technology to fabricate such a material then, and his work was ignored. It was not until

twenty-nine years later that J. B. Pendry revisited V. G. Veselago’s theory and published

a paper [9] about an artificial metallic construction that exhibited negative relative

permittivity εr. In 2001, Smith [10] conducted a demonstration that a structure consisting

of split-ring resonators (SRR) and wires can represent V. G. Veselago’s theory. From

then on, interest in MTMs grew, and many papers on applications of MTMs have been

published.

6

Left-handed materials like metal wires and split-ring resonators are intrinsically

lossy and narrowband [12]. Another method of achieving LH material with lower loss

and wider bandwidth is based on transmission-line theory. The periodic structure consists

of unit cells of square metal patches with a via to the ground plane. Metal caps below the

metal patches provide the capacitive coupling with adjacent patches, as shown in Figure

3. The via provides inductance to ground.

Figure 3. (a) Planar LH distributed periodic structure and its (b) unit cell (From [12]).

The structure presented in [12] shows strong LH properties due to series

capacitance provided by an extra layer of metal caps, but the reactance of the cap shifts

the operational frequency lower. The structure is isotropic in two dimensions when the

operational wavelength is large compared to the size of the unit cell. The structure can be

anisotropic if the unit cell is rectangular (rather than square) or if the metal-cap shape is

changed to get different capacitance values in different directions. The absolute value of

refractive index decreases as frequency increases and become less than one in the fast-

wave region where the LH phase velocity is greater than in air.

It is noted in reference [13] that an array of thin metallic wires creates a negative

permittivity medium, and an array of SRRs creates the resonant form of effective

magnetic permeability. Together they provide LH properties that can be seen only when

the EM propagation is in a direction with E

parallel to the wires and H

parallel to the

ring axis. When the system length is less than ten unit cells, transmission quickly

oscillates and decreases exponentially, due to large complex index of refraction.

7

C. THESIS OBJECTIVE

The objective of this thesis is to design a suitable unit-cell pattern to be used on a

structure to create an attenuation or induce absorption for a specific radar frequency. The

application for this MTM will be to reduce the radar signature of ships and aircraft. The

layers must be as thin and lightweight as possible. Unlike many other MTM applications,

loss is desired for this RAM. The X-band (8–12 GHz) has been selected as the frequency

band of interest for this study. Microwave Studio (MWS) software by CST was used to

model different types of MTMs over the frequency band of interest.

D. THESIS OUTLINE

A brief introduction to military radar, the background of MTMs and a literature

review were given in Chapter I. The unique properties of MTMs that emerge when they

interact with EM waves are explained in Chapter II. Included in Chapter II is a brief

history of a common type of MTM based on the split-ring resonator. Modeling and

simulation of the various designs of MTM unit cell is done in Microwave Studio, as

shown in Chapter III. The various results achieved are discussed and compared in

Chapter IV. The conclusions of the research, recommendations on applications and

suggestions for future studies are presented in Chapter V.

8


9

II. METAMATERIALS

A. INTRODUCTION

In this chapter, the basic concepts of MTM are discussed. The first is what

material and configurations are classified as MTM. The second is how MTM interacts

with EM waves. For example, Snell’s law of refraction, which refers to refraction

encountered when EM waves or light passes from one medium to another must be

amended. Third, there is the possibility of negative real parts of the permittivity and

permeability, the two electrical parameters that define a medium.

B. DOUBLE-NEGATIVE MATERIAL

It should be pointed out that MTMs include a wide variety of synthetic materials

with inclusions or structures. Often MTMs are referred to as double-negative material,

although some can be single-negative (SNG). DNG refers to material with simultaneous

negative real parts of the permittivity r and permeability r . The negative values

found in MTMs give them the unique property of negative refraction (elaborated upon in

the next section). The and of a material are usually expressed as their complex

relative terms, as defined in Equations (1.1) and (1.2).

The imaginary parts of r and r are responsible for losses in the MTM due to

electric and magnetic damping and finite conductivity [14]. MTMs fall into a variety of

classifications, such as chiral, homogeneous, inhomogeneous, isotropic, anisotropic, and

bianisotropic. In most materials, permittivity and permeability are described by scalar

values. For anisotropic material, they can only be described by a matrix or dyadic. In

matrix notation,

xx xy xz

r yx yy yz

zx zy zz

(2.1)

and

10

xx xy xz

r yx yy yz

zx zy zz

(2.2)

where the elements in the matrix are the complex relative values that fully describe the

permittivity and permeability [15]. The vast majority of MTMs have only diagonal

elements in Equations (2.1) and (2.2):

0 0

0 0

0 0

x

y

z

; (2.3)

0 0

0 0

0 0

x

y

z

. (2.4)

The permittivity and permeability for a lossless DNG material can also be written

as [16]

r r rj (2.5)

and

r r rj . (2.6)

Therefore, the wavenumber is [17]

0o r o r o r o r r rk k (2.7)

where 0 0 0k c and c = 2.998 x 108 m/s. The intrinsic impedance of the

medium is

r

ro o

r r

(2.8)

where 0 0 0 .

11

C. RETRIEVAL OF AND FROM S11 AND S21

To retrieve ε and , refer to the paper by Xudong Chen et al. [18], where the S-

parameters are expressed in terms of the reflection and transmission coefficients as

11S R (2.9)

and

021

jk dS Te (2.10)

where d is the thickness of the material under test. The wave impedance Z and the

refractive index n are related to S11 and S21 by

2 211 21

2 211 21

1

1

S SZ

S S

(2.11)

and

0 0

0

1Im 2 Rejnk d jnk dn ln e m j ln e

k d (2.12)

where m is an integer related to the branch index of the real part of n. The value of

0jnk de is derived from

0 21

11

11

1

jnk d Se

ZS

Z

. (2.13)

In reference [18], it is also mentioned that the correct sign of Z can be determined

by the relationship of Z and n. Two cases to correctly find the sign of Z are identified.

The first case is for Re Z , where is positive and for which Re 0Z . The

second case is to choose the sign of Z so that the corresponding Im 0n , or 0 1jnk de .

The method to accurately determine the branch of Re n is described in [18]. With Z and

n determined, ε can be found from the relation

n

Z (2.14)

and found from

nZ . (2.15)

12

D. NEGATIVE REFRACTION AND LEFTHANDEDNESS

The phenomenon of negative refraction is usually illustrated with an obliquely

incident wave from a double-positive (DPS) material into a double-negative material and

exiting to a double-positive material, as illustrated in Figure 4. Snell’s law for a lossless

DPS-DNG boundary can be written as

1

2

sin

sini

r

n

n

. (2.16)

tk

ik

rk

Figure 4. Obliquely incident wave propagation from DPS-DNG-DPS. Notice that the wave bends to the same side as the incident wave (After [19]).

The wave vectors (ray directions) for the incident, reflected, and transmitted fields

are [19]

1 ˆˆcos sini i ik k z x

1 ˆˆcos sinr i ik k z x

(2.17)

2 ˆˆcos sint t tk k z x

where 1 1 1k and 2 2 2k .

Incident wave

DPS 1n

DNG - 2n

x

z

DPS 1n

i r

13

The Poynting vectors are

2

1

1ˆˆcos sin

2o

i i i

ES z x

2

1

1ˆˆcos sin

2o

r i i

RES z x

(2.18)

2

2

1ˆˆcos sin

2o

t t t

TES z x

where R and T are the reflection and transmission coefficients, respectively, and oE is the

amplitude of the incident wave. The impedances are defined in accordance with Equation

(2.8).

When waves propagate in DPS materials, the Poynting vector and wavefront

velocity vector are in the same direction. If a wave propagates in a DNG material with a

negative index, the Poynting and wave vectors are

2 ˆˆcos sint t tk n z xc

(2.19)

and

2

2

1ˆˆcos sin

2o

t t t

TES z x

n

. (2.20)

These equations show that the wave vector points in the opposite direction of the power

flow, the Poynting vector being directed in a causal direction away from the interface.

This property is referred to as lefthandedness.

E. SPLIT-RING RESONATOR

Much current research and experimentation is based on the SRR. It is a good

structure to illustrate how the magnetic properties of a MTM are achieved. The SRR

design was derived from square arrays of concentric cylinders, as proposed by Pendry et

al. in 1999 [20]. The structure is made of metallic films wound on a cylinder, but with a

discontinuity (an axial slit) to prevent current from flowing azimuthally around the

14

cylinder, as seen in Figure 5. The metallic films are separated by a small distance to

create capacitance that allows current to flow, as depicted in Figure 6.

Figure 5. Cylinders with internal structures. Metallic films separated by distance d. There is a small gap at every film that prevents current from flowing around the

“ring” (From [20]).

Figure 6. Plan view of the cylinder. When the cylinder encounters a magnetic field parallel to it, current is induced. Current is proportional to the capacitance of the

structure (After [20]).

The capacitance in the structure balances out the inductance present when the

cylinder is placed in a square array. The metallic cylinders in the square array induce

d

+ + - + - -

+ + - -

+ + - -

- - + - + +

- - + +

- - + +

iout

iin

s = 0

15

current along the length of the cylinder if an electric field is not parallel to it. This creates

undesirable anisotropic behavior. To obtain isotropic behavior, the structure is modified

to have a series of flat disks that retain the split-ring configuration. They can be observed

as the concentric square structure in Figure 2. They are also referred to as coplanar rings

(CPRs).

The structure of the SRR exhibits negative permeability, while an array of wires

exhibits negative permittivity. To create a structure with both negative permittivity and

permeability, a wire is inserted behind the SRR [11], as shown in Figure 2. This

represents an example of V. G. Veselago’s left-hand material, as demonstrated by Smith

et al. in 2001 [10].

F. SUMMARY

The theory and formulation of double-negative materials and the propagation of

EM waves in a material with negative refractive index were presented in this chapter. The

working principle of a common design of MTM, the SRR, was reviewed. In the next

chapter, the modeling of the MTM design in MWS and the simulation setup parameters

are explained.

16


17

III. MODELING AND SIMULATION SETUP

A. INTRODUCTION

Using a computer simulation for product design greatly enhances productivity and

reduces the time and cost of research. The computer simulation program of choice was

MWS by CST. In this research, different MTM designs are simulated, and the original

design from [22] is modified to improve performance. The modeling of MTM designs

and the setup of the parameters used in simulations are described in detail in this chapter.

B. CST MICROWAVE STUDIO (MWS)

MWS was chosen because it provides fast, efficient analysis and design of EM

components, including printed circuit boards (PCBs). This software is based on the finite

integration technique (FIT) that requires the discretization of the entire calculation

volume. The calculation volume includes the MTM structure plus some additional

surrounding free space.

The software is capable of importing designs and diagrams drawn in other

software formats. MWS parameterizes imported CAD files. It uses an advanced ACIS-

based parametric modeling front end with structure visualization, and the software also

has a materials database.

MWS has multiple solvers: transient (time domain), frequency domain,

eigenmode, integral equation, multilayer, and hybrid (ray tracing). The transient solver in

MWS is the main simulation mode used for this research. This solver is suitable for most

high frequency applications and can obtain the entire broadband frequency behavior of

the simulated device in just one calculation run. An excellent feature in the transient

solver is the linear scaling of computational resources with structure size. This feature

allows the calculation of large arrays of elements based on a unit-cell design where

periodicity of the structure is taken into account [21].

18

C. BASELINE DESIGN

The model for this research was based on a design described in [22], shown in

Figure 7. This particular design is appealing because of its simultaneous absorption and

low reflection. It is a window structure designed to operate with free-space on both sides.

Part of the design modification is to make this structure operate as a coating over a

platform surface. The selected frequency is 11.5 GHz.

The design is derived from conventional coplanar rings and wires. Electric

coupling was supplied from the electric-ring resonator (ERR) [23]. The structure in

Figure 7(a) can be considered two coplanar split rings connected by the inductive ring

parallel to the split wire. This design was used instead of a conventional split-wire design

because a split-wire design is limited, other than the addition of more wires per unit cell,

for increasing its inductance [24]. Magnetic coupling was created with flux from the

circulating charges perpendicular to the propagation vector. This response was created by

combining the center wire of the ERR with a cut wire separated by the substrate, as

shown in Figures 7(b) and 7(c). The magnetic response can be tuned by changing the

geometry of the cut wire and substrate thickness. By manipulating the magnetic coupling

without changing the ERR, permittivity and permeability can be decoupled, and each

resonance can be individually tuned [22]. The dimensions (in millimeters) as given in the

paper are listed in Table 2.

Figure 7. (a) A front view of the resonator, (b) back view of the wire and (c) oblique view of the unit cell with direction of propagation in z (From [22]).

Center conductor

19

Table 2. Value of parameters used in the design from [22].


1a 4.2

2a 12.0

W 3.9

G 0.606

t 0.6

L 1.7

H 11.8



Wire thickness 0.017

Separation distance between layers 0.65


The authors state that FR-4 is used as the substrate, but they did not specify the

permittivity and loss tangent. Typical values for the permittivity of FR-4 range from 3.65

to 5.20. The loss tangent ranges from 0.013 to 0.025. In the simulations, a permittivity of

4.4 and loss tangent of 0.021 were used. In the many simulations that follow, it was

noticed that the loss tangent did not have much of an effect on the results. The

permittivity of the substrate has a noticeable effect on the results. Generally, when the

permittivity of the substrate was increased in simulations, the reflection coefficient

scattering parameter S11 increased while the transmission coefficient scattering parameter

S21 decreased. The opposite happened when permittivity was decreased. The specific

values are not critical, as it is possible to redesign the MTMs to give low S11 and low S21.

Therefore, a medium value of 4.4 was chosen for permittivity.

The frequency for the transient solver spans 0 to 25 GHz. The settings in MWS

for the boundary conditions and background properties used in simulations are as per

Figure 8 (a) and (b), respectively. A simulation was run in MWS, which gave good

agreement with the published results.

20

(a) (b)

Figure 8. (a) Setup of the boundary conditions and (b) background properties used in MWS simulations (From [21]).

Different values and combinations of the parameters L, H, t (in Figure 7) and the

separation of the substrate were tested to observe the results. Generally, the achieved

results are near the frequency for absorption or absorption level of the results reported in

[22].

A variety of modifications to the design in [22] were done, and some are shown in

Figure 9. In all, the different values of the thickness, width of conductor, and separation

of substrate in the new designs were tested. The most promising results are seen in Figure

9 (c) and (e), so more testing was done on these two designs. Other boundary conditions

for the simulation, as described in detail in the next section, were also applied to make

sure that the results converged and are consistent.

21

(a) (b) (c)

(d) (e) (f)

Figure 9. Several variations of the baseline design (a)–(f) that were tested. As shown here, three pieces of each design were simulated with waveguide ports.

D. OTHER BOUNDARY CONDITIONS

The initial testing for all the designs was done with the boundary conditions as in

Figure 8 (a) and simulated using the transient solver. The boundary conditions have Etan =

0 on the Xmax and Xmin sides and Htan = 0 on the Ymax and Ymin sides. This simulates a

plane wave with Ex and Hy. This configuration can only simulate normal incident angles

but can do a broadband calculation of S-parameters from one single calculation run by

applying discrete Fourier transforms to the time signals [21]. This configuration was also

22

used with the frequency domain solver to verify convergence and accuracy. The

frequency domain solver has options for periodic boundary conditions and the use of

Floquet modes for non-normal incidence angles.

1. Periodic Boundary Condition

Periodic boundary conditions are used to simulate an infinite structure of the unit-

cell design. This is done in the frequency-domain solver. For this mode of simulation, in

the “Boundary Conditions” setting box, the Xmin, Xmax, Ymin and Ymax are set to

“Periodic.” Zmin and Zmax are set to “Open (add space).”

2. Unit-cell Boundary Condition

Floquet modes are used to simulate oblique angles of incidence on the infinite

structure of the design. This is done in the frequency-domain solver. This approach can

obtain accurate results at very oblique angles of incidence (close to grazing) [25]. For this

mode of simulation, in the “Boundary Conditions” setting box, the Xmin, Xmax, Ymin and

Ymax are set to “Unit Cell.” Zmin and Zmax are set to “Open (add space).” Different “Theta”

and “Phi” angles for simulation can also be specified in “Phase Shift/Scan Angles.”

E. PORTS

Optimization of the parameters of the design is done with two ports, one in front,

facing the three-layered unit cell, and one behind, facing the back of the three-layered

unit cell. The ports are where the model is excited (stimulated) and the response (output)

fields monitored. This configuration, depicted in Figure 10, is to compute the reflection

coefficient S11 and transmission coefficient S21 parameters. S11 and S22 are the reflection

coefficients of the material under test (e.g. S11 means transmitting from port 1 and

receiving at port 1). S12 and S21 refer to the transmission coefficients of the material under

test. (e.g. S12 means transmitting from port 2 and receiving at port 1).

The layer or coating configuration, shown in Figure 11, uses only one port, the

one that faces the unit cell from the front. The back of the three-layered unit cell has a

23

metallic plate 0.85 mm away. This is used to simulate the actual application where the

MTM structure is applied onto the platform as a coating. The skin of the platform is the

metallic plate.

Figure 10. Two-port configuration used to compute the S11 and S12 parameters.

Figure 11. Single port configuration used to compute S11 for a coating application.

Overall thickness of metamaterial structure

Reference Plane

Metallic backing

Port 2

Port 1

24

F. THE REFERENCE PLANE

The distance between the reference planes of the two ports defines the electrical

thickness of the whole MTM structure. The reference plane can be specified when

defining the ports. The phase and amplitude references for S11 and S12 are taken at the

point where the reference plane is defined, which is not necessarily at the port. If no

reference planes are defined, the references are taken at ports 1 and 2. The results for the

simulations in the next chapter are taken with the reference planes defined at 4 mm away

from the unit cell, as shown in Figure 12.

(a) (b)

Figure 12. (a) Definition of waveguide port 1. (b) Definition of waveguide port 2.

25

In this chapter, the modeling details of the MTM and the setup configurations for

simulations in MWS using different boundary conditions were described. In the next

chapter, the results obtained in the simulations are presented and analyzed.

26


27

IV. SIMULATION RESULTS AND DATA ANALYSIS

The simulation results for two main MTM designs that came closest to the

performance objectives are presented in this chapter. An explanation of the different

parameters that are tuned to achieve the desired results is also included.

A. DESIGN (C)

As mentioned, the baseline design for this research is based on [22], shown in

Figure 9 (c). Subsequently we refer this as Design (c). Modifications were made to

several of the parameters. The final design has maximum absorption at 11.5 GHz, close

to 11.65 GHz of [22]. The final dimensions of Design (c) are shown in Table 3. The CST

model is shown in Figure 13. How the final design was derived are explained in the

following sections.

Table 3. Final parameters used in simulation for the results of Design (c). Parameters are defined in Figure 7.


1a 4.2

2a 12.0

W 3.9

G 0.606

t 0.8

L 0.64

H 11.8




Wire thickness 0.15

Separation distance between layers 1.7

Number of unit-cell layers 3 pieces

28

Figure 13. Design (c): the final design.

1. Length of Wire

Three simulations whose S22 and S12 results are depicted in Figures 14–16, are for

substrates of lengths 8 mm, 12 mm, and 16 mm, respectively. The wire on the backside

was 0.2 mm shorter than the substrate. The results in Figures 14–16 were simulated with

the parameters in Table 3 (Figure 7), except H. As seen in Figure 14, when the wire is

short, there is a peak of transmittivity (S12) close to 11 GHz. As the length of the wire

increases, this peak shifts to a lower frequency. The size of the unit cell was to be kept

compact, so a long wire as in Figure 16 was not favorable. A long wire creates high

reflectivity (S22). The best result is seen in Figure 15, where there is low S12 at the

frequency where S22 is the smallest of the three lengths. This means that the reduction in

S22 is not due to the material being transparent to the EM wave, but rather to the

material’s more efficient absorption of EM waves at 11.5 GHz. Notice the peak

absorption shifts to a higher frequency as the length of wire increases.

Center conductor

Wire

Gap

Conductor, Upper “C”

Conductor, Lower “C”

29

Figure 14. Simulated S-parameters for a wire of 7.8 mm in length.

Figure 15. Simulated S-parameters for a wire of 11.8 mm in length (optimum).



30

Figure 16. Simulated S-parameters for a wire of 15.8 mm in length.

2. Width of Wire

The results in Figures 17–20 were simulated with parameters as in Table 3, except

wire width L. They show that the wire width also has an impact on the results. As the

wire gets thinner, S22 decreases until the wire is 0.64 mm. When the width is less than

0.64 mm, S22 increases. The null also shifts to a higher frequency with reduced width.

This is one of the parameters that can be used to tune the structure for the frequency of

absorption.


31

Figure 17. Simulated S-parameters for a wire width of 1.7 mm, as used in [22].

Figure 18. Simulated S-parameters for a wire width of 1.0 mm.



32



3. Thickness of Wire and Separation Distance Between Unit Cells

The effect of increasing the thickness of the wire and separation distance can be

seen in Figures 21–23. Notice that the frequency location of the S22 null shifts higher as

wire thickness and separation distance increased.



33

Figure 21. Simulated S-parameters for a wire thickness of 0.017 mm with unit-cell separation of 0.65 mm.




34


4. Number of Layers

The results for different numbers of unit-cell layers are shown in Figures 24–26.

With two layers, the magnitude of the S22 is 0.062 as compared to a magnitudes of 0.042

and 0.035 for three and four layers, respectively. Three layers of unit cells were chosen as

optimal because the difference in the result, compared with that of four layers, was very

small, and the requirement is to keep the thickness as small as possible. The fewer layers

there are, the less weight and thickness.


35

Figure 24. Simulated S-parameters for two layers.

Figure 25. Simulated S-parameters for three layers.



36

Figure 26. Simulated S-parameters for four layers.

5. Conductor Width

Next, the conductor width is varied keeping all other parameters constant. The

effect of changing the width of conductor t is shown in Figures 27–29. It is seen that the

optimal width lies at 0.8 mm.

Figure 27. Simulated S-parameters for a conductor width of 0.6 mm.



37





38

6. Conductor Thickness

The effect of conductor thickness on the S-parameters is shown in Figures 30 and

31. Increasing the thickness of the conductor did not give a better result because of the

increase in resistance. Therefore, the conductor thickness remains per the design in [22],

t = 0.017 mm.

Figure 30. Simulated S-parameters for a conductor thickness per original design, 0.017 mm.

Figure 31. Simulated S-parameters when the conductor thickness is increased to 0.05 mm.



39

7. Center Conductor

The results in Figures 32–34 are based on the original design in [22] but with a

change in the length of the center conductor. The center conductor length was increased

beyond the initial design. With a 1-mm extension of the center conductor, the null of S22

is deeper (see Figure 33) as compared to the initial design (shown in Figure 32). With a

2-mm extension, the result was like the initial design, but with a shift of frequency.

Hence, the design of a 1-mm extension of the center conductor was selected.

Figure 32. Simulated S-parameters per design in [22].

Figure 33. Simulated S-parameters per design in [22], but with center conductor extension of 1 mm.



40

Figure 34. Simulated S-parameters per design in [22], but with center conductor extending 2 mm.

8. Gap

The capacitance between the ends of the upper C and lower C in the design also

plays a part in optimizing the result. The null of S22 shifts to a higher frequency as the

gap increases. From Figures 35–37, it can be seen that a 0.606 mm gap gives the best

result.

Figure 35. Simulated S-parameters for a gap of 0.3 mm in the design.



41



9. Overall Performance

The width of the design was the only parameter that was not changed because this

dimension was targeted to work at the desired frequency band (X-band), 8–12 GHz. The

performance of Design (c) was impressive for normal incident angle, with results for S22

of 0.0418 (27.57 dB) and S12 of 0.0637 (23.91 dB). In reality, most of the time EM



42

waves do not impinge on the MTM at a normal incidence angles. Therefore, other

incident angles are also simulated. The performance for different and angles is

tabulated in Table 4 (linear). The Floquet modal analysis option in MWS was used to

obtain the data. A standard spherical polar coordinate system is used, as shown in Figure

38.

Figure 38. Coordinate system definition for non-normal incidence angles.

Design (c) is symmetrical in the x and y-planes; therefore, only one quadrant of

the results is simulated. Pattern results are as shown in Table 4 and Figures 39 to 41.

From the results, we can see that there is good absorption 20o from normal incidence

less than a 0.178 (15 dB) change. For the θ angles, there is less than 0.32 (10 dB)

change when = 0o, as shown in Figure 39. The results show that absorption decreases as

increases, regardless of θ. The design had very little absorption for large , as evident in

Figures 40 and 41.

When Design (c) was simulated with one port and a metallic backing, the result,

as shown in Figure 42, is similarly good, achieving reflectivity S11 of 0.02053 (33.75

dB) at a normal incidence angle. This is the usual material configuration when the design

z x

y

0o

θ, = 180o

, = 270o

90o

90o

43

is applied onto the surface of a platform. In the simulation, the metallic backing is at a

distance of 0.85 mm from the last unit-cell, and the reference plane is 0.5 mm in front of

the unit-cell facing the port.

The reference plane affects the level of the null but not the bandwidth or

frequency of absorption. If the reference plane were closer to the unit cell, the null would

be less by a few more decibels. The distance of the reference plane from the port affects

the phase of S11 and S12. This can also add or subtract a few decibels from the result. This

is due to the evanescent modes closer to the structure.

Table 4. Magnitude of reflected EM wave for oblique incidence on Design (c).

Magnitude of reflected EM wave

Theta (deg)

0 10 20 30 40 50 60 70 80

Phi (deg)

0 0.047 0.059 0.162 0.187 0.229 0.227 0.283 0.324 0.451

10 0.064 0.065

20 0.069 0.090

30 0.193 0.310

40 0.376 0.546

50 0.541 0.672

60 0.723 0.755

70 0.855 0.755

80 0.943 0.944

90 0.974 0.974 0.973 0.968 0.958 0.938 0.899 0.909 0.957

= 0o Graph in Figure 39. θ = 0o Graph in Figure 40.

= θ Graph in Figure 41.

44

Figure 39. Magnitude of S11 at different θ with = 0o.

Figure 40. Magnitude of S11 at different with θ = 0o.

Figure 41. Magnitude of S11 when θ equals .

45

(a)

(b)

Figure 42. (a) Design (c) with metallic backing, a configuration likely during application on a platform. (b) Result from this configuration. S11 has a value equivalent to a reduction of 33.75 dB. S12 is zero, due to the metallic backing, no transmission

through a metallic surface.


46

B. DESIGN (E)

Design (e) was conceived in the process of searching for better results than

Design (c). A strip of conductor between the upper and bottom “Cs” was added as a way

to increase capacitance. The width of this strip is also t, and the gap between this strip

and the upper and bottom “C” is still G.

Promising results were obtained with initial simulations. Due to time constraints,

detailed simulations to explore the full performance of Design (e) were not done. The

result for the S11 and S21 parameters are shown in Figure 43. The null of this design is at

9.0 GHz.

The parameters used in the simulation of Design (e) are shown in Table 5.

Table 5. Parameters used in the simulation of Design (e).


1a 4.2

2a 12.0

W 3.9

G 0.606

t 0.9

L 0.9

H 11.8




Wire thickness 0.15

Separation distance between unit cell 1.7


47

Figure 43. Simulated S-parameters for S11 and S21 of Design (e).

C. SUMMARY

In this chapter, the design parameters were changed to find the optimal

dimensions for each parameter. The dimensions of Design (c) are given in Table 3. The

overall performance of Design (c) was evaluated at different incident angles. The results

show that Design (c) works well for 20o from the normal, yielding 15 dB of reduction,

or more.

The width of the wire, thickness of the wire, separation distance between unit

cells, conductor width, and center conductor length significantly affect the frequency

where absorption occurs. To design a MTM for a specific frequency, we determined the

frequency of choice and tuned the various parameters to make the reflectivity as low as

possible. If absorption for another frequency band is required, the size of the whole

design must be scaled accordingly; generally, larger for lower frequency bands and

smaller for higher frequency bands.


48


49

V. RECOMMENDATIONS AND CONCLUSION

In this chapter, a summary of the research and results for the final design are

presented. This chapter concludes with recommendations for future research in the area

of MTMs for radar frequencies.

A. SUMMARY AND CONCLUSIONS

The objective of this study was to find a new MTM design for X-band radar

frequencies that could be applied to a metallic surface. Hence, this thesis described the

design, modeling and simulation of a new MTM, which is a modification of the design in

[22]. A detailed description of Design (c) was given, with dimensions in Table 3, so that

future researchers will be able to replicate the results and continue the study.

In the optimization of the different parameters of the new design, it was noticed

that the absorption frequency is determined by many parameters but mainly by the

dimensions of the cell because the dimension W is proportional to the wavelength and

determines which band the absorption lies in. Other parameters, like width of wire,

thickness of wire, separation distance between unit cells, conductor width, and center

conductor, can also affect the absorption frequency, but these parameters are used to fine

tune the frequency of absorption and the absorption level.

It has been shown that high absorption can be achieved at normal incidence. The

optimal values for the important design parameters have been presented, with a look into

how each particular parameter value was chosen. The overall result obtained for Design

(c) was 0.0418 (27.57 dB) for S22, together with a low value of 0.0637 (23.91 dB) for

S12. This design was also simulated with a metallic backing, as would be present in an

actual application onto a platform. The S11 result achieved for normal incidence is

0.02053 (33.75 dB).

In the course of this study, questions were raised that could not be addressed due

to time constraints. These questions are detailed below for future investigation. It was

shown with Design (e) that better performance in some areas is possible.

50

B. RECOMMENDATION FOR FUTURE STUDIES

Through the course of this research, several issues were raised as to how the

performance of the final design can be improved and made applicable to a platform.

These questions are described, future studies and possible solutions are recommended in

the following subsections.

1. EM Transparent Material Between Unit Cells

Simulations for Design (c) were conducted with a vacuum between the unit cell

layers. In the actual fabrication of the structure, the space between the unit cells will be

filled by support material. A low dielectric foam can be used without having any impact

on the performance. Other possible materials are a thin silicon or polyurethane layer. The

permittivity and permeability of these materials will significantly affect the performance,

so the layers will have to be included in the MWS simulation to get a more realistic

design. A possible implementation using spacers is shown in Figure 44.

(a) (b)

Figure 44. (a) Side view of material. (b) Plan view of material. Design (c) incorporated with EM transparent material spacer. (a) and (b) simulate a large sheet of the

metamaterial with Design (c) cascaded horizontally and vertically.

A 0.5mm space in front of the metamaterial acts as a protection against erosion, and, on the back, gives distance between material and platform.

EM transparent material as spacer

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2. Dual-Polarization Design

Design (c) is strictly for vertical polarization; the design works only when the

incident wave is vertically polarized. For horizontal polarization, the design does not give

any absorption at all. Application for a single-polarization absorber is limited, so

modification of Design (c) to handle both horizontal and vertical polarizations should be

looked into. References [26] and [27] suggest designs for dual polarization. Some

possible designs are shown in Figure 45.

(a) (b) (c)

Figure 45. Possible designs for dual polarization.

3. Wideband Absorption

A wideband absorber is favorable since it covers more radar frequencies. Design

(c) has absorption of almost 30 dB at 11.5 GHz (dual port measurement), but it is a

narrowband absorber with a 10 dB bandwidth of 191 MHz. Most radars hop their

frequency to prevent being jammed; therefore, a wider bandwidth of absorption is

necessary to truly defeat a radar’s detection. An example of a wideband absorber, even

though the average absorption level is only 10 dB is given in [26].

4. Circuit Equivalent of Design (c)

Future work to verify the results of Design (c) would be to develop a circuit

equivalent. Simulations can be done in Agilent Advance Design System (ADS). A good

start is given in [28]. A possible circuit equivalent to Design (c) is shown in Figure 46.

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Figure 46. A possible circuit-equivalent model to Design (c).

5. Extracting and from Scattering Parameters S11 and S12

From the results of the simulation it is possible to extract the effective permittivity

and permeability from the complex S11 and S12 data. Using the extracted permittivity and

permeability, we can define and simulate a block of material with these properties as bulk

material. Both simulations should give the same result. A Matlab code to extract the

permittivity and permeability must be written for this application.

0 V or Ground + V

53

LIST OF REFERENCES

[1] http://www.aewa.org/Library/rf_bands.html (Accessed: 8/16/12).

[2] A. Noor, Z. Hu, “Cloaking of metallic sub-wavelength objects by plasmonic metamaterial shell in quasistatic limit,” IET Microwaves, Antennas & Propagation, vol 3, no.1, pp. 40–46, 2009.

[3] Yan Liu, Xiao Wei, HuanQing Wang, ZhuZhen Li, HongCheng Yin, PeiKang

Huang, ”Backscattering of metamaterial electromagnetic cloak,” 2008 International Workshop on Metamaterials, pp. 335–337, 2008.

[4] Fei Ding, Yanxia Cui, Xiaochen Ge, Yi Jin, and Sailing He, “Ultra-broadband

microwave metamaterial absorber,” Appl. Phys. Lett. vol. 100, paper 103506, 2012.

[5] V.G. Veselago, “The electrodynamic properties of a mixture of electric and

magnetic charges,” Soviet Physics Journal of Experimental and Theoretical Physics, vol. 25, pp. 680,1967.

[6] Lee, H.S., Park, J.W., Lee, H.M., “Design of double negative metamaterial

absorber cells using electromagnetic-field coupled resonators,” Microwave Conference Proceedings (APMC), 2011 Asia-Pacific, pp. 1062–1065, 2011.

[7] Varadan, V.V., “Radar Absorbing Applications of Metamaterials,” Region 5

Technical Conference, 2007 IEEE, Digital Object Identifier: 10.1109/TPSD.2007.4380361, pp. 105–108, 2007.

[8] V. G. Veselago, “The electrodynamics of substances with simultaneously

negative values of ε and μ,” Sov. Phys. Uspekhi , vol. 10, no. 4, pp. 509–514, 1968. [Usp. Fiz.Nauk, vol. 92, pp. 517–526, 1967].

[9] J. B. Pendry, A. J. Holden, W. J. Stewart and I. Youngs, “Extremely Low

Frequency Plasmons in Metallic Mesostrucrures,” Phy. Rev. Letters, vol 76, no, 25, pp. 4773–4776, 1996.

[10] R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser and S. Schultz, “Microwave

transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett., vol 78, no. 4, pp. 489, 2001.

[11] Ilya Shadrivov and Yuri Kivshar, “Bending waves in a wrong way,” The Pyhsicist, vol 41, no. 4, pp. 137, 2004.

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[12] Atsushi Sanada, Christophe Carloz and Tatsuo Itoh, “Planar distributed structures

with negative refractive index,” IEEE Trans. on Microwave theory and techniques, vol 52, no. 4, pp.1252–1263, 4 April 2004.

[13] Peter Markos and C.M. Soukoulis, “Transmission properties and effective

electromagnetic parameters of double negative metamaterials,” Optics express, vol.11, no. 7, pp. 649–661, 7 April 2003.

[14] R. Gómez Martín, Electromagnetic field theory for physicists and engineers:

Fundamentals and Applications, Granada, pp. 21, Físicas Curso 2006–2007. [15] D. C. Jenn, Notes for EC3630 (Radiowave Propagation), Naval Postgraduate

School, 2003 (unpublished). [16] Nader Engheta and Richard W. Ziolkowski, “A positive future for double-

negative metamaterials,” IEEE Trans. Microwave Theory Tech., vol 53, no. 4, 2005.

[17] Bo-Kai, Feng, “Extracting material constitutive parameters from scattering parameters,” Naval Postgraduate School Thesis, Sep. 2006.

[18] X.Chen, T. M. Grzegorczyk, B. I. Wu, J. Pacheco Jr., and J. A. Kong, “Robust Method to Retrieve the Constitutive Effective Parameters of Metamaterials,” Phys. Rev. E, vol. 70, paper 016608, 2004.

[19] Nader Engheta and Richard W. Ziolkowski, “Introduction, history, and selected

topics in fundamental theories of metamaterials,” in Metamaterials : Physics and Engineering Explorations, pp. 17–19, IEEE Explore Digital Library (2010), (Books - Metamaterials section). Retrieved 2010-05-01., John Wiley & Sons, Inc., 2006.

[20] J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from

Conductors and Enhanced Nonlinear Phenomena,” IEEE Trans. Microwave Theory Tech., vol 47, no.11, pp. 2075–2084, November 1999.

[21] Computer Simulation Technology, CST Microwave Studio – Getting Started,

Computer Simulation Technology, Darmstadt (Germany), pp. 4–6, 2005. [22] N. I. Landy, S. Sajuyigbe, J. J. Mock, D. R. Smith, and W. J. Padilla, “Perfect

Metamaterial Absorber,” Phys. Rev. Letters, vol. 100, paper 207402, 2008. [23] W. J. Padilla, M. T. Aronsson, C. Highstrete and Mark Lee, A. J. Taylor and R. D.

Averitt, “Electrically resonant terahertz metamaterials: Theoretical and experimental investigations,” Phy. Rev. B, vol 75, paper 041102 (R), 2007.

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[24] D. R. Smith, D. C. Vier, Willie Padilla, Syrus C. Nemat-Nasser, and S. Schultz, “Loop-wire medium for investigating plasmons at microwave frequencies,” Applied Physics Letters, vol 75, no. 10, pp. 1425, 1999.

[25] http://www.cst.com/Content/Applications/Article/Article.aspx?id=355 (Access :

8/1/2012). [26] A. Noor, Z. Hu, “Metamaterial dual polarised resistive Hilbert curve array radar

absorber,” IET Microwaves, Antennas & Propagation, vol 4, no.6, pp. 667–673, 2010.

[27] Youngsoo Jang, Joungyoung Lee, Sungjoon Lim, “Incident Angle Insensitive

Double Negative (DNG) Metamaterial Absorber,” Microwave Conference Proceedings (APMC), 2011 Asia-Pacific, pp. 1870–1872, 2011.

[28] Wakatsuchi, H., Paul, J., Greedy, S., Christopoulos, C., “Cut-Wire Metamaterial

Design Based on Simplified Equivalent Circuit Models,” IEEE Trans. on Antennas and Propagation, vol 60 , no. 8, pp. 3670–3678, 2012.

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INITIAL DISTRIBUTION LIST

1. Defense Technical Information Center Ft. Belvoir, Virginia

2. Dudley Knox Library Naval Postgraduate School Monterey, California

3. Professor R. Clark Robertson Chairman, Department of Electrical and Computer Engineering Naval Postgraduate School Monterey, California

4. Professor David C. Jenn

Department of Electrical and Computer Engineering Naval Postgraduate School Monterey, California

5. Dr James Calusdian Department of Electrical and Computer Engineering Naval Postgraduate School Monterey, California

6. Professor Yeo Tat Soon

Director, Temasek Defence System Institute (TDSI) National University of Singapore Singapore, Singapore

7. Ms Tan Lai Poh

Senior Manager, Temasek Defence System Institute (TDSI) National University of Singapore Singapore, Singapore

8. Mr Fong Saik Hay CTO, ST Engrg, ST Engineering Singapore, Singapore

9. Mr R. Balakrishnan

Vice President, VTE Singapore Technologies Aerospace Limited Singapore, Singapore

naval postgraduate school · modeling and simulation are done in microwave studio by computer ......

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